What is the limit as x approaches 0 of 5/x+5/(x^2-x) ?

The limit as x approaches 0 of 5/x+5/(x^2-x) is -5

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limit as x approaches 0 of 5/x+5/(x^2-x)

x \to 0 lim (\frac{5}{x} + \frac{5}{x ^{2} - x})

- 5

Solution steps

x \to 0 lim (\frac{5}{x} + \frac{5}{x ^{2} - x})

Multiply by the conjugate of

\frac{5}{x} + \frac{5}{x ^{2} - x} : \frac{\frac{25}{x ^{2}} - \frac{25}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{5}{x} - \frac{5}{x ^{2} - x}}

= x \to 0 lim (\frac{\frac{25}{x ^{2}} - \frac{25}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{5}{x} - \frac{5}{x ^{2} - x}})

Simplify

\frac{\frac{25}{x ^{2}} - \frac{25}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{5}{x} - \frac{5}{x ^{2} - x}} : \frac{5}{x - 1}

= x \to 0 lim (\frac{5}{x - 1})

Plug in the value

x = 0

= \frac{5}{0 - 1}

Simplify

= - 5

x \to 0 lim (\frac{x}{cot ( x )})

x \to 0 lim (x ∣ x ∣)

x \to 1 lim (3 x^{2} + 3)

x \to \infty lim (- 10)

x \to 0 lim (\frac{1}{ln ( e ^{x} - 1 )})

What is the limit as x approaches 0 of 5/x+5/(x^2-x) ?
The limit as x approaches 0 of 5/x+5/(x^2-x) is -5